Subgroups — C₇×#61198 #13238414

Order 1792.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3328	C₂	1	2	yes	maximal, complemented
4	C₇×#3322	C₂	1	2	yes	maximal, complemented
5	C₇×#3321	C₂	1	2	yes	maximal, complemented
6	C₇×#3320	C₂	1	2	yes	maximal, complemented
7	C₇×#3315	C₂	1	2	yes	maximal, complemented
8	C₇×#3311	C₂	1	2	yes	maximal, complemented
9	C₇×#3303	C₂	1	2	yes	maximal, complemented
10	C₇×#3300	C₂	1	2	yes	maximal, complemented
11	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×#135	C₂²	1	1	yes	characteristic
28	C₂×C₇×#135	C₂²	1	1	yes	characteristic
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
31	C₇×#556	—	2	1	no	—
32	C₇×#556	C₂²	1	2	yes	—
33	C₇×#555	—	2	1	no	—
34	C₇×#555	C₂²	1	2	yes	complemented
35	C₇×#553	—	2	1	no	—
36	C₇×#553	C₂²	1	2	yes	—
37	C₇×#552	—	2	1	no	—
38	C₇×#552	C₂²	1	2	yes	complemented
39	C₇×D₄×Q₈	C₂²	1	2	yes	—
40	C₇×#548	C₂²	1	2	yes	—
41	C₇×#547	—	2	2	no	—
42	C₇×#547	C₂²	1	2	yes	—
43	C₇×#546	—	2	2	no	—
44	C₇×#546	C₂²	1	2	yes	—
45	C₇×#544	C₂²	1	1	yes	characteristic, complemented
46	C₇×#538	—	2	2	no	—
47	C₇×#537	—	2	1	no	—
48	C₇×#537	C₂²	1	1	yes	characteristic
49	C₇×#537	C₂²	1	1	yes	characteristic, complemented
50	C₇×#536	—	2	1	no	—
51	C₇×#536	C₂²	1	1	yes	characteristic
52	C₇×#529	—	2	2	no	—
53	C₇×#525	—	2	1	no	—
54	C₇×#525	C₂²	1	1	yes	characteristic
55	C₇×#525	C₂²	1	1	yes	characteristic
56	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
57	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#520	C₂²	1	1	yes	characteristic, complemented
60	C₇×#520	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₇×#117	C₂²	1	1	yes	characteristic
62	C₇×#491	C₂²	1	2	yes	complemented
63	C₇×#489	C₂²	1	2	yes	complemented
64	C₇×#488	C₂²	1	2	yes	complemented
65	C₇×#487	C₂²	1	2	yes	complemented
66	C₇×#485	C₂²	1	2	yes	—
67	C₇×#485	C₂²	1	2	yes	—
68	C₇×#485	C₂²	1	2	yes	complemented
69	C₇×#485	C₂²	1	2	yes	complemented
70	C₇×#485	C₂²	1	2	yes	complemented
71	C₇×#484	C₂²	1	2	yes	complemented
72	C₇×#482	C₂²	1	2	yes	complemented
73	C₇×#480	C₂²	1	2	yes	complemented
74	C₇×#479	C₂²	1	2	yes	complemented
75	C₇×#478	C₂²	1	2	yes	complemented
76	C₇×#476	C₂²	1	2	yes	complemented
77	C₇×#475	C₂²	1	2	yes	complemented
78	C₇×#470	C₂²	1	2	yes	—
79	C₇×#470	C₂²	1	2	yes	complemented
80	C₇×#469	C₂²	1	2	yes	complemented
81	C₇×#468	C₂²	1	2	yes	—
82	C₇×#467	C₂²	1	2	yes	complemented
83	C₇×#465	C₂²	1	2	yes	complemented
84	C₇×#465	C₂²	1	2	yes	complemented
85	C₇×#465	C₂²	1	2	yes	complemented
86	C₇×#464	C₂²	1	2	yes	complemented
87	C₇×#463	C₂²	1	2	yes	complemented
88	C₇×#462	C₂²	1	2	yes	complemented
89	C₇×#461	C₂²	1	2	yes	complemented
90	C₇×#452	C₂²	1	1	yes	characteristic
91	C₇×#452	C₂²	1	1	yes	characteristic
92	C₇×#452	C₂²	1	2	yes	complemented
93	C₇×#451	C₂²	1	1	yes	characteristic
94	C₇×#451	C₂²	1	2	yes	complemented
95	C₇×#450	C₂²	1	1	yes	characteristic
96	C₇×#449	C₂²	1	1	yes	characteristic
97	C₇×#449	C₂²	1	1	yes	characteristic
98	C₇×#449	C₂²	1	2	yes	complemented
99	C₇×#448	C₂²	1	1	yes	characteristic
100	C₇×#448	C₂²	1	2	yes	complemented
101	C₇×#447	C₂²	1	1	yes	characteristic
102	C₇×#440	C₂²	1	2	yes	complemented
103	C₇×#440	C₂²	1	2	yes	complemented
104	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
105	C₄×C₇×D₈	C₂²	1	2	yes	complemented
106	C₇×#436	C₂²	1	2	yes	—
107	C₇×#435	C₂²	1	2	yes	—
108	C₇×#435	C₂²	1	2	yes	complemented
109	C₇×C₈×D₄	C₂²	1	2	yes	complemented
110	C₇×#428	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
113	C₇×#424	C₂²	1	1	yes	characteristic, complemented
114	C₇×#419	C₂²	1	2	yes	—
115	C₇×#419	C₂²	1	1	yes	characteristic, complemented
116	C₇×#419	C₂²	1	2	yes	complemented
117	C₇×#418	C₂²	1	2	yes	—
118	C₇×#417	C₂²	1	1	yes	characteristic
119	C₇×#417	C₂²	1	1	yes	characteristic
120	C₇×#417	C₂²	1	1	yes	characteristic
121	C₇×#417	C₂²	1	1	yes	characteristic
122	C₇×#417	C₂²	1	1	yes	characteristic, complemented
123	C₇×#417	C₂²	1	2	yes	complemented
124	C₇×#416	C₂²	1	1	yes	characteristic
125	C₇×#416	C₂²	1	1	yes	characteristic
126	C₇×#416	C₂²	1	2	yes	—
127	C₇×#416	C₂²	1	2	yes	—
128	C₇×#416	C₂²	1	2	yes	complemented
129	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₇×#103	C₂²	1	2	yes	complemented
131	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
132	C₇×#408	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₇×#405	C₂²	1	1	yes	characteristic, complemented
135	#61198	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₇×2₋¹⁺⁴	—	2	4	no	—
137	C₇×2₋¹⁺⁴	—	4	2	no	—
138	C₂×C₇×#41	—	2	1	no	—
139	C₂×C₇×#41	—	2	2	no	—
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	—	2	4	no	—
143	C₂×C₇×#41	—	4	2	no	—
144	C₂×C₇×#41	C₂³	1	1	yes	characteristic
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂×C₇×#41	C₂³	1	1	yes	characteristic
147	C₂×C₇×#41	C₂³	1	1	yes	characteristic
148	C₂×C₇×#41	C₂³	1	2	yes	—
149	C₂×C₇×#41	C₂³	1	1	yes	characteristic
150	C₂×C₇×#41	C₂³	1	1	yes	characteristic
151	C₂²×C₇×Q₈	—	2	1	no	—
152	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
154	C₂²×C₇×Q₈	C₂³	1	2	yes	—
155	C₂²×C₇×D₄	—	2	1	no	—
156	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₇	—	2	1	no	—
158	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
159	C₇×#137	—	4	2	no	—
160	C₇×#135	—	2	4	no	—
161	C₇×#135	—	4	2	no	—
162	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
163	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
164	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
166	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
167	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
168	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
169	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
170	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
171	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
172	C₇×#131	—	4	2	no	—
173	C₂×C₇×M₁₆	—	4	2	no	—
174	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
175	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
176	C₂×C₇×M₁₆	C₂³	1	2	yes	—
177	C₂×C₇×M₁₆	C₂³	1	2	yes	—
178	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
179	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
180	C₂²×C₇×C₈	C₂³	1	2	yes	—
181	C₂²×C₇×C₈	C₂³	1	2	yes	—
182	C₇×C₄⋊Q₈	—	2	2	no	—
183	C₇×C₄⋊Q₈	—	2	1	no	—
184	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
185	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
186	C₇×#126	—	2	2	no	—
187	C₇×#126	—	2	2	no	—
188	C₇×#126	—	2	2	no	—
189	C₇×#126	—	2	2	no	—
190	C₇×#125	—	2	2	no	—
191	C₇×#125	—	2	1	no	—
192	C₇×#125	C₂³	1	2	yes	—
193	C₇×#124	—	2	2	no	—
194	C₇×#124	—	2	2	no	—
195	C₇×#124	—	2	2	no	—
196	C₇×#124	—	2	2	no	—
197	C₇×#124	C₂³	1	2	yes	—
198	C₇×#123	—	2	2	no	—
199	C₇×#123	—	2	1	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	—	2	2	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×#123	D₄	1	2	yes	—
206	C₇×C₂²⋊Q₈	—	2	1	no	—
207	C₇×C₂²⋊Q₈	—	2	1	no	—
208	C₇×C₂²⋊Q₈	—	2	1	no	—
209	C₇×C₂²⋊Q₈	—	2	1	no	—
210	C₇×C₂²⋊Q₈	—	2	1	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	—	2	1	no	—
213	C₇×C₂²⋊Q₈	—	2	2	no	—
214	C₇×C₂²⋊Q₈	—	2	2	no	—
215	C₇×C₂²⋊Q₈	—	2	2	no	—
216	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
217	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
218	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₇×#121	—	2	1	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	2	no	—
227	C₇×#121	—	2	2	no	—
228	C₇×#121	—	2	2	no	—
229	C₇×#121	—	2	1	no	—
230	C₇×#121	—	2	2	no	—
231	C₇×#121	—	2	2	no	—
232	C₇×#121	—	2	2	no	—
233	C₇×#121	D₄	1	1	yes	characteristic
234	C₇×#121	D₄	1	1	yes	characteristic
235	C₇×#121	C₂³	1	1	yes	characteristic
236	C₇×#121	C₂³	1	2	yes	—
237	C₇×#121	C₂³	1	2	yes	—
238	C₇×#121	C₂³	1	1	yes	characteristic
239	C₇×#120	—	2	1	no	—
240	C₇×#120	—	2	2	no	—
241	C₇×#120	D₄	1	2	yes	—
242	C₄×C₇×Q₈	—	2	1	no	—
243	C₄×C₇×Q₈	—	2	2	no	—
244	C₄×C₇×Q₈	C₂³	1	2	yes	—
245	C₄×C₇×Q₈	C₂³	1	2	yes	—
246	C₄×C₇×D₄	—	2	2	no	—
247	C₄×C₇×D₄	—	2	1	no	—
248	C₄×C₇×D₄	—	2	2	no	—
249	C₄×C₇×D₄	—	2	1	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	—	2	2	no	—
252	C₄×C₇×D₄	—	2	2	no	—
253	C₄×C₇×D₄	—	2	2	no	—
254	C₄×C₇×D₄	—	2	2	no	—
255	C₄×C₇×D₄	C₂³	1	2	yes	—
256	C₄×C₇×D₄	C₂³	1	2	yes	—
257	C₄×C₇×D₄	C₂³	1	2	yes	—
258	C₄×C₇×D₄	C₂³	1	2	yes	—
259	C₇×#117	—	2	1	no	—
260	C₇×#117	—	2	1	no	—
261	C₇×#117	—	2	1	no	—
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	2	no	—
264	C₇×#117	—	2	2	no	—
265	C₇×#117	C₂³	1	2	yes	—
266	C₇×#117	C₂³	1	2	yes	—
267	C₇×#117	C₂³	1	2	yes	—
268	C₇×#117	C₂³	1	1	yes	characteristic
269	C₇×#117	C₂³	1	1	yes	characteristic
270	C₂×C₇×C₄⋊C₄	—	2	1	no	—
271	C₂×C₇×C₄⋊C₄	—	2	1	no	—
272	C₂×C₇×C₄⋊C₄	—	2	1	no	—
273	C₂×C₇×C₄⋊C₄	—	2	2	no	—
274	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
275	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₄²×C₇	—	2	1	no	—
282	C₇×#107	C₂³	1	2	yes	—
283	C₇×#107	C₂³	1	2	yes	—
284	C₇×#107	C₂³	1	2	yes	—
285	C₇×#106	C₂³	1	2	yes	—
286	C₇×#106	C₂³	1	2	yes	—
287	C₇×#106	C₂³	1	2	yes	—
288	C₇×C₄⋊C₈	C₂³	1	2	yes	—
289	C₇×C₄⋊C₈	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	1	yes	characteristic
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#103	C₂³	1	2	yes	—
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#103	C₂³	1	2	yes	—
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#103	C₂³	1	1	yes	characteristic
304	C₇×#103	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×#102	C₂³	1	2	yes	—
309	C₇×#102	C₂³	1	1	yes	characteristic
310	C₇×#102	C₂³	1	1	yes	characteristic
311	C₇×#102	C₂³	1	2	yes	—
312	C₇×#102	C₂³	1	1	yes	characteristic
313	C₇×#102	C₂³	1	2	yes	—
314	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
319	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
320	C₇×#97	C₂³	1	2	yes	—
321	C₄×C₇×C₈	C₂³	1	2	yes	—
322	#3493	C₂×C₇	1	1	yes	characteristic, complemented
323	#3489	C₂×C₇	1	1	yes	characteristic, complemented
324	#3328	C₂×C₇	1	2	yes	complemented
325	#3322	C₂×C₇	1	2	yes	complemented
326	#3321	C₂×C₇	1	2	yes	complemented
327	#3320	C₂×C₇	1	2	yes	complemented
328	#3315	C₂×C₇	1	2	yes	complemented
329	#3311	C₂×C₇	1	2	yes	complemented
330	#3303	C₂×C₇	1	2	yes	complemented
331	#3300	C₂×C₇	1	2	yes	complemented
332	#3137	C₂×C₇	1	1	yes	characteristic, complemented
333	#3098	C₂×C₇	1	1	yes	characteristic, complemented
334	C₂×#485	C₂×C₇	1	1	yes	characteristic, complemented
335	#3084	C₂×C₇	1	1	yes	characteristic, complemented
336	#3060	C₂×C₇	1	1	yes	characteristic, complemented
337	#3056	C₂×C₇	1	1	yes	characteristic, complemented
338	#3046	C₂×C₇	1	1	yes	characteristic, complemented
339	#3013	C₂×C₇	1	1	yes	characteristic, complemented
340	#3002	C₂×C₇	1	1	yes	characteristic, complemented
341	#2951	C₂×C₇	1	1	yes	characteristic, complemented
342	#2933	C₂×C₇	1	1	yes	characteristic, complemented
343	#2898	C₂×C₇	1	1	yes	characteristic, complemented
344	#2896	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	1	no	—
346	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
347	C₇×#41	—	2	2	no	—
348	C₇×#41	—	2	2	no	—
349	C₇×#41	—	2	2	no	—
350	C₇×#41	—	2	2	no	—
351	C₇×#41	—	2	2	no	—
352	C₇×#41	—	2	4	no	—
353	C₇×#41	—	2	2	no	—
354	C₇×#41	—	2	2	no	—
355	C₇×#41	—	2	2	no	—
356	C₇×#41	—	2	2	no	—
357	C₇×#41	—	4	4	no	—
358	C₇×#41	—	4	1	no	—
359	C₇×#41	—	4	1	no	—
360	C₇×#41	—	4	2	no	—
361	C₇×#41	—	4	4	no	—
362	C₇×#41	—	4	4	no	—
363	C₇×#41	—	4	8	no	—
364	C₇×#41	#41	1	4	yes	—
365	C₂×C₇×Q₈	—	2	1	no	—
366	C₂×C₇×Q₈	—	2	2	no	—
367	C₂×C₇×Q₈	—	2	1	no	—
368	C₂×C₇×Q₈	—	2	2	no	—
369	C₂×C₇×Q₈	—	2	2	no	—
370	C₂×C₇×Q₈	—	2	4	no	—
371	C₂×C₇×Q₈	—	2	2	no	—
372	C₂×C₇×Q₈	—	2	2	no	—
373	C₂×C₇×Q₈	—	4	1	no	—
374	C₂×C₇×Q₈	—	4	2	no	—
375	C₂×C₇×Q₈	—	4	4	no	—
376	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
377	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
378	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
379	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₇×D₄	—	2	1	no	—
382	C₂×C₇×D₄	—	2	2	no	—
383	C₂×C₇×D₄	—	2	1	no	—
384	C₂×C₇×D₄	—	2	2	no	—
385	C₂×C₇×D₄	—	2	1	no	—
386	C₂×C₇×D₄	—	2	1	no	—
387	C₂×C₇×D₄	—	2	1	no	—
388	C₂×C₇×D₄	—	2	2	no	—
389	C₂×C₇×D₄	—	2	1	no	—
390	C₂×C₇×D₄	—	2	1	no	—
391	C₂×C₇×D₄	—	2	2	no	—
392	C₂×C₇×D₄	—	2	1	no	—
393	C₂×C₇×D₄	—	4	1	no	—
394	C₂×C₇×D₄	—	4	4	no	—
395	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
396	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
397	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
398	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
399	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
400	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
401	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₇	—	2	1	no	—
403	C₂²×C₄×C₇	—	2	2	no	—
404	C₂²×C₄×C₇	—	2	2	no	—
405	C₂²×C₄×C₇	—	2	1	no	—
406	C₂²×C₄×C₇	—	2	2	no	—
407	C₂²×C₄×C₇	—	2	1	no	—
408	C₂²×C₄×C₇	—	2	1	no	—
409	C₂²×C₄×C₇	—	2	1	no	—
410	C₂²×C₄×C₇	—	2	1	no	—
411	C₂²×C₄×C₇	—	2	2	no	—
412	C₂²×C₄×C₇	—	2	2	no	—
413	C₂²×C₄×C₇	—	2	1	no	—
414	C₂²×C₄×C₇	—	2	1	no	—
415	C₂²×C₄×C₇	—	2	1	no	—
416	C₂²×C₄×C₇	—	2	1	no	—
417	C₂²×C₄×C₇	—	2	2	no	—
418	C₂²×C₄×C₇	—	2	2	no	—
419	C₂²×C₄×C₇	—	4	4	no	—
420	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
421	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
422	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
423	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
424	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
427	C₇×Q₁₆	—	2	2	no	—
428	C₇×Q₁₆	—	4	1	no	—
429	C₇×Q₁₆	—	4	2	no	—
430	C₇×SD₁₆	—	2	2	no	—
431	C₇×SD₁₆	—	2	2	no	—
432	C₇×SD₁₆	—	4	1	no	—
433	C₇×SD₁₆	—	4	1	no	—
434	C₇×SD₁₆	—	4	2	no	—
435	C₇×D₈	—	2	2	no	—
436	C₇×D₈	—	4	1	no	—
437	C₇×M₁₆	—	2	2	no	—
438	C₇×M₁₆	—	2	2	no	—
439	C₇×M₁₆	—	4	2	no	—
440	C₇×M₁₆	—	4	2	no	—
441	C₂×C₇×C₈	—	2	2	no	—
442	C₂×C₇×C₈	—	2	2	no	—
443	C₂×C₇×C₈	—	4	2	no	—
444	C₂×C₇×C₈	—	4	2	no	—
445	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
446	C₂×C₇×C₈	C₂⁴	1	2	yes	—
447	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
448	C₂×C₇×C₈	C₂⁴	1	2	yes	—
449	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
450	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
451	C₇×C₄⋊C₄	—	2	2	no	—
452	C₇×C₄⋊C₄	—	2	1	no	—
453	C₇×C₄⋊C₄	—	2	1	no	—
454	C₇×C₄⋊C₄	—	2	2	no	—
455	C₇×C₄⋊C₄	—	2	2	no	—
456	C₇×C₄⋊C₄	—	2	2	no	—
457	C₇×C₄⋊C₄	—	2	2	no	—
458	C₇×C₄⋊C₄	—	2	2	no	—
459	C₇×C₄⋊C₄	—	2	1	no	—
460	C₇×C₄⋊C₄	—	2	2	no	—
461	C₇×C₄⋊C₄	—	2	1	no	—
462	C₇×C₄⋊C₄	—	2	2	no	—
463	C₇×C₄⋊C₄	—	2	2	no	—
464	C₇×C₄⋊C₄	—	2	1	no	—
465	C₇×C₄⋊C₄	—	2	2	no	—
466	C₇×C₄⋊C₄	—	2	2	no	—
467	C₇×C₄⋊C₄	—	2	2	no	—
468	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
469	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
470	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
471	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
472	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
473	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
474	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
475	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
476	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
477	C₇×C₂²⋊C₄	—	2	2	no	—
478	C₇×C₂²⋊C₄	—	2	2	no	—
479	C₇×C₂²⋊C₄	—	2	2	no	—
480	C₇×C₂²⋊C₄	—	2	2	no	—
481	C₇×C₂²⋊C₄	—	2	2	no	—
482	C₇×C₂²⋊C₄	—	2	1	no	—
483	C₇×C₂²⋊C₄	—	2	2	no	—
484	C₇×C₂²⋊C₄	—	2	1	no	—
485	C₇×C₂²⋊C₄	—	2	1	no	—
486	C₇×C₂²⋊C₄	—	2	2	no	—
487	C₇×C₂²⋊C₄	—	2	2	no	—
488	C₇×C₂²⋊C₄	—	2	2	no	—
489	C₇×C₂²⋊C₄	—	2	1	no	—
490	C₇×C₂²⋊C₄	—	2	2	no	—
491	C₇×C₂²⋊C₄	—	2	2	no	—
492	C₇×C₂²⋊C₄	—	2	2	no	—
493	C₇×C₂²⋊C₄	—	2	1	no	—
494	C₇×C₂²⋊C₄	—	2	2	no	—
495	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
496	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
497	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
498	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
499	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
500	C₄²×C₇	—	2	2	no	—
501	C₄²×C₇	—	2	2	no	—
502	C₄²×C₇	—	2	2	no	—
503	C₄²×C₇	—	2	2	no	—
504	C₄²×C₇	—	2	2	no	—
505	C₄²×C₇	—	2	1	no	—
506	C₄²×C₇	C₂⁴	1	2	yes	—
507	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
508	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
509	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
510	C₂×#135	C₂²×C₇	1	1	yes	characteristic
511	C₂×#135	C₂²×C₇	1	1	yes	characteristic
512	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
513	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
514	#556	—	2	1	no	—
515	#556	C₂²×C₇	1	2	yes	—
516	#555	—	2	1	no	—
517	#555	C₂²×C₇	1	2	yes	complemented
518	#553	—	2	1	no	—
519	#553	C₂²×C₇	1	2	yes	—
520	#552	—	2	1	no	—
521	#552	C₂²×C₇	1	2	yes	complemented
522	D₄×Q₈	C₂²×C₇	1	2	yes	—
523	#548	C₂²×C₇	1	2	yes	—
524	#547	—	2	2	no	—
525	#547	C₂²×C₇	1	2	yes	—
526	#546	—	2	2	no	—
527	#546	C₂²×C₇	1	2	yes	—
528	#544	C₂²×C₇	1	1	yes	characteristic, complemented
529	#538	—	2	2	no	—
530	#537	—	2	1	no	—
531	#537	C₂²×C₇	1	1	yes	characteristic
532	#537	C₂²×C₇	1	1	yes	characteristic, complemented
533	#536	—	2	1	no	—
534	#536	C₂²×C₇	1	1	yes	characteristic
535	#529	—	2	2	no	—
536	#525	—	2	1	no	—
537	#525	C₂²×C₇	1	1	yes	characteristic
538	#525	C₂²×C₇	1	1	yes	characteristic
539	C₂×C₂²⋊Q₈	—	2	1	no	—
540	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
541	#520	C₂²×C₇	1	1	yes	characteristic
542	#520	C₂²×C₇	1	1	yes	characteristic, complemented
543	#520	C₂²×C₇	1	1	yes	characteristic, complemented
544	C₂×#117	C₂²×C₇	1	1	yes	characteristic
545	#491	C₂²×C₇	1	2	yes	complemented
546	#489	C₂²×C₇	1	2	yes	complemented
547	#488	C₂²×C₇	1	2	yes	complemented
548	#487	C₂²×C₇	1	2	yes	complemented
549	#485	C₂²×C₇	1	2	yes	—
550	#485	C₂²×C₇	1	2	yes	—
551	#485	C₂²×C₇	1	2	yes	complemented
552	#485	C₂²×C₇	1	2	yes	complemented
553	#485	C₂²×C₇	1	2	yes	complemented
554	#484	C₂²×C₇	1	2	yes	complemented
555	#482	C₂²×C₇	1	2	yes	complemented
556	#480	C₂²×C₇	1	2	yes	complemented
557	#479	C₂²×C₇	1	2	yes	complemented
558	#478	C₂²×C₇	1	2	yes	complemented
559	#476	C₂²×C₇	1	2	yes	complemented
560	#475	C₂²×C₇	1	2	yes	complemented
561	#470	C₂²×C₇	1	2	yes	—
562	#470	C₂²×C₇	1	2	yes	complemented
563	#469	C₂²×C₇	1	2	yes	complemented
564	#468	C₂²×C₇	1	2	yes	—
565	#467	C₂²×C₇	1	2	yes	complemented
566	#465	C₂²×C₇	1	2	yes	complemented
567	#465	C₂²×C₇	1	2	yes	complemented
568	#465	C₂²×C₇	1	2	yes	complemented
569	#464	C₂²×C₇	1	2	yes	complemented
570	#463	C₂²×C₇	1	2	yes	complemented
571	#462	C₂²×C₇	1	2	yes	complemented
572	#461	C₂²×C₇	1	2	yes	complemented
573	#452	C₂²×C₇	1	1	yes	characteristic
574	#452	C₂²×C₇	1	1	yes	characteristic
575	#452	C₂²×C₇	1	2	yes	complemented
576	#451	C₂²×C₇	1	1	yes	characteristic
577	#451	C₂²×C₇	1	2	yes	complemented
578	#450	C₂²×C₇	1	1	yes	characteristic
579	#449	C₂²×C₇	1	1	yes	characteristic
580	#449	C₂²×C₇	1	1	yes	characteristic
581	#449	C₂²×C₇	1	2	yes	complemented
582	#448	C₂²×C₇	1	1	yes	characteristic
583	#448	C₂²×C₇	1	2	yes	complemented
584	#447	C₂²×C₇	1	1	yes	characteristic
585	#440	C₂²×C₇	1	2	yes	complemented
586	#440	C₂²×C₇	1	2	yes	complemented
587	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
588	C₄×D₈	C₂²×C₇	1	2	yes	complemented
589	#436	C₂²×C₇	1	2	yes	—
590	#435	C₂²×C₇	1	2	yes	—
591	#435	C₂²×C₇	1	2	yes	complemented
592	C₈×D₄	C₂²×C₇	1	2	yes	complemented
593	#428	C₂²×C₇	1	1	yes	characteristic, complemented
594	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
595	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
596	#424	C₂²×C₇	1	1	yes	characteristic, complemented
597	#419	C₂²×C₇	1	2	yes	—
598	#419	C₂²×C₇	1	2	yes	complemented
599	#419	C₂²×C₇	1	1	yes	characteristic, complemented
600	#418	C₂²×C₇	1	2	yes	—
601	#417	C₂²×C₇	1	1	yes	characteristic
602	#417	C₂²×C₇	1	1	yes	characteristic
603	#417	C₂²×C₇	1	1	yes	characteristic
604	#417	C₂²×C₇	1	1	yes	characteristic
605	#417	C₂²×C₇	1	2	yes	complemented
606	#417	C₂²×C₇	1	1	yes	characteristic, complemented
607	#416	C₂²×C₇	1	1	yes	characteristic
608	#416	C₂²×C₇	1	1	yes	characteristic
609	#416	C₂²×C₇	1	2	yes	—
610	#416	C₂²×C₇	1	2	yes	—
611	#416	C₂²×C₇	1	2	yes	complemented
612	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
613	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
614	C₂×#103	C₂²×C₇	1	2	yes	complemented
615	#408	C₂²×C₇	1	1	yes	characteristic, complemented
616	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
617	#405	C₂²×C₇	1	1	yes	characteristic, complemented
618	C₂³×C₇	—	2	1	no	—
619	C₂³×C₇	—	2	2	no	—
620	C₂³×C₇	—	2	1	no	—
621	C₂³×C₇	—	2	1	no	—
622	C₂³×C₇	—	4	1	no	—
623	C₂³×C₇	—	4	1	no	—
624	C₂³×C₇	—	4	2	no	—
625	C₂³×C₇	—	4	2	no	—
626	C₂³×C₇	—	8	1	no	—
627	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
628	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
629	C₂³×C₇	C₂²×D₄	1	2	yes	—
630	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
631	C₇×Q₈	—	2	2	no	—
632	C₇×Q₈	—	2	1	no	—
633	C₇×Q₈	—	2	1	no	—
634	C₇×Q₈	—	2	2	no	—
635	C₇×Q₈	—	2	1	no	—
636	C₇×Q₈	—	2	1	no	—
637	C₇×Q₈	—	2	2	no	—
638	C₇×Q₈	—	2	1	no	—
639	C₇×Q₈	—	4	4	no	—
640	C₇×Q₈	—	4	2	no	—
641	C₇×Q₈	—	4	2	no	—
642	C₇×Q₈	—	8	2	no	—
643	C₇×Q₈	C₂×#41	1	2	yes	—
644	C₇×D₄	—	2	4	no	—
645	C₇×D₄	—	2	4	no	—
646	C₇×D₄	—	2	2	no	—
647	C₇×D₄	—	2	1	no	—
648	C₇×D₄	—	2	1	no	—
649	C₇×D₄	—	2	1	no	—
650	C₇×D₄	—	2	1	no	—
651	C₇×D₄	—	2	1	no	—
652	C₇×D₄	—	4	2	no	—
653	C₇×D₄	—	4	2	no	—
654	C₇×D₄	—	4	2	no	—
655	C₇×D₄	—	4	2	no	—
656	C₇×D₄	—	4	2	no	—
657	C₇×D₄	—	4	4	no	—
658	C₇×D₄	—	4	2	no	—
659	C₇×D₄	—	4	2	no	—
660	C₇×D₄	—	8	2	no	—
661	C₇×D₄	—	8	1	no	—
662	C₇×D₄	—	8	2	no	—
663	C₇×D₄	—	8	1	no	—
664	C₇×D₄	C₂×#41	1	2	yes	—
665	C₂×C₄×C₇	—	2	2	no	—
666	C₂×C₄×C₇	—	2	1	no	—
667	C₂×C₄×C₇	—	2	2	no	—
668	C₂×C₄×C₇	—	2	2	no	—
669	C₂×C₄×C₇	—	2	4	no	—
670	C₂×C₄×C₇	—	2	1	no	—
671	C₂×C₄×C₇	—	2	1	no	—
672	C₂×C₄×C₇	—	2	2	no	—
673	C₂×C₄×C₇	—	2	1	no	—
674	C₂×C₄×C₇	—	2	2	no	—
675	C₂×C₄×C₇	—	2	1	no	—
676	C₂×C₄×C₇	—	2	2	no	—
677	C₂×C₄×C₇	—	2	1	no	—
678	C₂×C₄×C₇	—	2	1	no	—
679	C₂×C₄×C₇	—	2	2	no	—
680	C₂×C₄×C₇	—	2	2	no	—
681	C₂×C₄×C₇	—	2	1	no	—
682	C₂×C₄×C₇	—	2	2	no	—
683	C₂×C₄×C₇	—	2	1	no	—
684	C₂×C₄×C₇	—	4	2	no	—
685	C₂×C₄×C₇	—	4	2	no	—
686	C₂×C₄×C₇	—	4	2	no	—
687	C₂×C₄×C₇	—	4	4	no	—
688	C₂×C₄×C₇	—	4	4	no	—
689	C₂×C₄×C₇	—	4	2	no	—
690	C₂×C₄×C₇	—	4	2	no	—
691	C₂×C₄×C₇	—	4	2	no	—
692	C₂×C₄×C₇	—	8	2	no	—
693	C₂×C₄×C₇	—	8	2	no	—
694	C₂×C₄×C₇	—	8	1	no	—
695	C₂×C₄×C₇	—	8	2	no	—
696	C₂×C₄×C₇	—	8	1	no	—
697	C₂×C₄×C₇	—	8	1	no	—
698	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
699	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
700	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
701	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
702	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
703	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
704	C₂×C₄×C₇	C₂×#41	1	2	yes	—
705	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
706	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
707	C₇×C₈	—	2	1	no	—
708	C₇×C₈	—	2	1	no	—
709	C₇×C₈	—	2	1	no	—
710	C₇×C₈	—	2	1	no	—
711	C₇×C₈	—	2	2	no	—
712	C₇×C₈	—	2	2	no	—
713	2₋¹⁺⁴	—	2	4	no	—
714	2₋¹⁺⁴	—	4	2	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	2	2	no	—
717	C₂×#41	—	2	1	no	—
718	C₂×#41	—	2	1	no	—
719	C₂×#41	—	2	4	no	—
720	C₂×#41	—	4	2	no	—
721	C₂×#41	C₂³×C₇	1	1	yes	characteristic
722	C₂×#41	C₂³×C₇	1	1	yes	characteristic
723	C₂×#41	C₂³×C₇	1	2	yes	—
724	C₂×#41	C₂³×C₇	1	1	yes	characteristic
725	C₂×#41	C₂³×C₇	1	1	yes	characteristic
726	C₂×#41	C₂³×C₇	1	1	yes	characteristic
727	C₂×#41	C₂³×C₇	1	1	yes	characteristic
728	C₂²×Q₈	—	2	1	no	—
729	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
730	C₂²×Q₈	C₂³×C₇	1	2	yes	—
731	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
732	C₂²×D₄	—	2	1	no	—
733	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
734	C₂³×C₄	—	2	1	no	—
735	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
736	#137	—	4	2	no	—
737	#135	—	2	4	no	—
738	#135	—	4	2	no	—
739	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
740	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
741	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
745	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
746	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
747	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
748	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
749	#131	—	4	2	no	—
750	C₂×M₁₆	—	4	2	no	—
751	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
752	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
753	C₂×M₁₆	C₂³×C₇	1	2	yes	—
754	C₂×M₁₆	C₂³×C₇	1	2	yes	—
755	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
756	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
757	C₂²×C₈	C₂³×C₇	1	2	yes	—
758	C₂²×C₈	C₂³×C₇	1	2	yes	—
759	C₄⋊Q₈	—	2	2	no	—
760	C₄⋊Q₈	—	2	1	no	—
761	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
762	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#126	—	2	2	no	—
767	#125	—	2	2	no	—
768	#125	—	2	1	no	—
769	#125	C₂³×C₇	1	2	yes	—
770	#124	—	2	2	no	—
771	#124	—	2	2	no	—
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	C₂³×C₇	1	2	yes	—
775	#123	—	2	2	no	—
776	#123	—	2	1	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	C₇×D₄	1	2	yes	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
794	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
795	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
796	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
797	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
798	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
801	#121	—	2	1	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	C₇×D₄	1	1	yes	characteristic
811	#121	C₇×D₄	1	1	yes	characteristic
812	#121	C₂³×C₇	1	1	yes	characteristic
813	#121	C₂³×C₇	1	1	yes	characteristic
814	#121	C₂³×C₇	1	2	yes	—
815	#121	C₂³×C₇	1	2	yes	—
816	#120	—	2	1	no	—
817	#120	—	2	2	no	—
818	#120	C₇×D₄	1	2	yes	—
819	C₄×Q₈	—	2	1	no	—
820	C₄×Q₈	—	2	2	no	—
821	C₄×Q₈	C₂³×C₇	1	2	yes	—
822	C₄×Q₈	C₂³×C₇	1	2	yes	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	C₂³×C₇	1	2	yes	—
833	C₄×D₄	C₂³×C₇	1	2	yes	—
834	C₄×D₄	C₂³×C₇	1	2	yes	—
835	C₄×D₄	C₂³×C₇	1	2	yes	—
836	#117	—	2	1	no	—
837	#117	—	2	1	no	—
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	—	2	2	no	—
841	#117	—	2	2	no	—
842	#117	C₂³×C₇	1	2	yes	—
843	#117	C₂³×C₇	1	2	yes	—
844	#117	C₂³×C₇	1	1	yes	characteristic
845	#117	C₂³×C₇	1	2	yes	—
846	#117	C₂³×C₇	1	1	yes	characteristic
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	—	2	2	no	—
851	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
852	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
853	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
854	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
855	C₂×C₂²⋊C₄	—	2	1	no	—
856	C₂×C₂²⋊C₄	—	2	1	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	C₂×C₄²	—	2	1	no	—
859	#107	C₂³×C₇	1	2	yes	—
860	#107	C₂³×C₇	1	2	yes	—
861	#107	C₂³×C₇	1	2	yes	—
862	#106	C₂³×C₇	1	2	yes	—
863	#106	C₂³×C₇	1	2	yes	—
864	#106	C₂³×C₇	1	2	yes	—
865	C₄⋊C₈	C₂³×C₇	1	2	yes	—
866	C₄⋊C₈	C₂³×C₇	1	2	yes	—
867	#103	C₂³×C₇	1	1	yes	characteristic
868	#103	C₂³×C₇	1	2	yes	—
869	#103	C₂³×C₇	1	2	yes	—
870	#103	C₂³×C₇	1	2	yes	—
871	#103	C₂³×C₇	1	2	yes	—
872	#103	C₂³×C₇	1	2	yes	—
873	#103	C₂³×C₇	1	2	yes	—
874	#103	C₂³×C₇	1	2	yes	—
875	#103	C₂³×C₇	1	2	yes	—
876	#103	C₂³×C₇	1	2	yes	—
877	#103	C₂³×C₇	1	1	yes	characteristic
878	#103	C₂³×C₇	1	1	yes	characteristic
879	#103	C₂³×C₇	1	1	yes	characteristic
880	#103	C₂³×C₇	1	2	yes	—
881	#103	C₂³×C₇	1	2	yes	—
882	#102	C₂³×C₇	1	1	yes	characteristic
883	#102	C₂³×C₇	1	2	yes	—
884	#102	C₂³×C₇	1	2	yes	—
885	#102	C₂³×C₇	1	2	yes	—
886	#102	C₂³×C₇	1	2	yes	—
887	#102	C₂³×C₇	1	1	yes	characteristic
888	#102	C₂³×C₇	1	1	yes	characteristic
889	#102	C₂³×C₇	1	1	yes	characteristic
890	#102	C₂³×C₇	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
892	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
893	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
894	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
895	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
896	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
897	#97	C₂³×C₇	1	2	yes	—
898	C₄×C₈	C₂³×C₇	1	2	yes	—
899	C₂²×C₇	—	2	1	no	—
900	C₂²×C₇	—	2	1	no	—
901	C₂²×C₇	—	2	2	no	—
902	C₂²×C₇	—	2	1	no	—
903	C₂²×C₇	—	2	1	no	—
904	C₂²×C₇	—	2	1	no	—
905	C₂²×C₇	—	2	2	no	—
906	C₂²×C₇	—	2	1	no	—
907	C₂²×C₇	—	2	1	no	—
908	C₂²×C₇	—	2	1	no	—
909	C₂²×C₇	—	2	2	no	—
910	C₂²×C₇	—	2	2	no	—
911	C₂²×C₇	—	4	1	no	—
912	C₂²×C₇	—	4	1	no	—
913	C₂²×C₇	—	4	1	no	—
914	C₂²×C₇	—	4	1	no	—
915	C₂²×C₇	—	4	1	no	—
916	C₂²×C₇	—	4	1	no	—
917	C₂²×C₇	—	4	1	no	—
918	C₂²×C₇	—	4	1	no	—
919	C₂²×C₇	—	8	2	no	—
920	C₂²×C₇	—	8	4	no	—
921	C₂²×C₇	#546	1	2	yes	—
922	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
923	C₄×C₇	—	2	2	no	—
924	C₄×C₇	—	2	2	no	—
925	C₄×C₇	—	2	1	no	—
926	C₄×C₇	—	2	1	no	—
927	C₄×C₇	—	2	2	no	—
928	C₄×C₇	—	2	2	no	—
929	C₄×C₇	—	4	2	no	—
930	C₄×C₇	—	4	2	no	—
931	C₄×C₇	—	4	1	no	—
932	C₄×C₇	—	4	2	no	—
933	C₄×C₇	—	4	1	no	—
934	C₄×C₇	—	4	1	no	—
935	C₄×C₇	—	4	2	no	—
936	C₄×C₇	—	4	1	no	—
937	C₄×C₇	#546	1	2	yes	—
938	C₄×C₇	C₂²×#41	1	1	yes	characteristic
939	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
940	C₂⁴	—	2	1	no	—
941	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	2	2	no	—
947	#41	—	2	4	no	—
948	#41	—	2	2	no	—
949	#41	—	2	2	no	—
950	#41	—	2	2	no	—
951	#41	—	2	2	no	—
952	#41	—	4	4	no	—
953	#41	—	4	1	no	—
954	#41	—	4	1	no	—
955	#41	—	4	2	no	—
956	#41	—	4	4	no	—
957	#41	—	4	4	no	—
958	#41	—	4	8	no	—
959	#41	C₇×#41	1	4	yes	—
960	C₂×Q₈	—	2	1	no	—
961	C₂×Q₈	—	2	2	no	—
962	C₂×Q₈	—	2	1	no	—
963	C₂×Q₈	—	2	2	no	—
964	C₂×Q₈	—	2	2	no	—
965	C₂×Q₈	—	2	4	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	—	2	2	no	—
968	C₂×Q₈	—	4	1	no	—
969	C₂×Q₈	—	4	2	no	—
970	C₂×Q₈	—	4	4	no	—
971	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
972	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
973	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
974	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
975	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	4	1	no	—
989	C₂×D₄	—	4	4	no	—
990	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
991	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
992	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
993	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
994	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
995	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
996	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	2	no	—
1013	C₂²×C₄	—	2	2	no	—
1014	C₂²×C₄	—	4	4	no	—
1015	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1016	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1017	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1019	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1022	Q₁₆	—	2	2	no	—
1023	Q₁₆	—	4	1	no	—
1024	Q₁₆	—	4	2	no	—
1025	SD₁₆	—	2	2	no	—
1026	SD₁₆	—	2	2	no	—
1027	SD₁₆	—	4	1	no	—
1028	SD₁₆	—	4	1	no	—
1029	SD₁₆	—	4	2	no	—
1030	D₈	—	2	2	no	—
1031	D₈	—	4	1	no	—
1032	M₁₆	—	2	2	no	—
1033	M₁₆	—	2	2	no	—
1034	M₁₆	—	4	2	no	—
1035	M₁₆	—	4	2	no	—
1036	C₂×C₈	—	2	2	no	—
1037	C₂×C₈	—	2	2	no	—
1038	C₂×C₈	—	4	2	no	—
1039	C₂×C₈	—	4	2	no	—
1040	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1041	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1042	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1043	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1044	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1045	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1065	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1066	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1067	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1068	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1069	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1070	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1071	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1091	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1092	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1093	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1094	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1095	C₄²	—	2	2	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	—	2	2	no	—
1100	C₄²	—	2	1	no	—
1101	C₄²	C₂⁴×C₇	1	2	yes	—
1102	C₂×C₇	—	2	2	no	—
1103	C₂×C₇	—	4	2	no	—
1104	C₂×C₇	—	4	1	no	—
1105	C₂×C₇	—	4	1	no	—
1106	C₂×C₇	—	4	2	no	—
1107	C₂×C₇	—	8	1	no	—
1108	C₂×C₇	—	8	1	no	—
1109	C₂×C₇	C₂×#546	1	1	yes	characteristic
1110	C₂×C₇	#3584	1	1	yes	characteristic
1111	C₂×C₇	#3586	1	1	yes	characteristic
1112	C₂³	—	2	1	no	—
1113	C₂³	—	2	2	no	—
1114	C₂³	—	2	1	no	—
1115	C₂³	—	2	1	no	—
1116	C₂³	—	4	1	no	—
1117	C₂³	—	4	1	no	—
1118	C₂³	—	4	2	no	—
1119	C₂³	—	4	2	no	—
1120	C₂³	—	8	1	no	—
1121	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1122	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1123	C₂³	C₂²×C₇×D₄	1	2	yes	—
1124	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1125	Q₈	—	2	1	no	—
1126	Q₈	—	2	2	no	—
1127	Q₈	—	2	1	no	—
1128	Q₈	—	2	2	no	—
1129	Q₈	—	2	1	no	—
1130	Q₈	—	2	1	no	—
1131	Q₈	—	2	2	no	—
1132	Q₈	—	2	1	no	—
1133	Q₈	—	4	4	no	—
1134	Q₈	—	4	2	no	—
1135	Q₈	—	4	2	no	—
1136	Q₈	—	8	2	no	—
1137	Q₈	C₂×C₇×#41	1	2	yes	—
1138	D₄	—	2	4	no	—
1139	D₄	—	2	4	no	—
1140	D₄	—	2	1	no	—
1141	D₄	—	2	1	no	—
1142	D₄	—	2	1	no	—
1143	D₄	—	2	1	no	—
1144	D₄	—	2	1	no	—
1145	D₄	—	2	2	no	—
1146	D₄	—	4	2	no	—
1147	D₄	—	4	2	no	—
1148	D₄	—	4	2	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	4	2	no	—
1151	D₄	—	4	4	no	—
1152	D₄	—	4	2	no	—
1153	D₄	—	4	2	no	—
1154	D₄	—	8	2	no	—
1155	D₄	—	8	1	no	—
1156	D₄	—	8	2	no	—
1157	D₄	—	8	1	no	—
1158	D₄	C₂×C₇×#41	1	2	yes	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	4	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	4	no	—
1182	C₂×C₄	—	4	4	no	—
1183	C₂×C₄	—	4	2	no	—
1184	C₂×C₄	—	4	2	no	—
1185	C₂×C₄	—	4	2	no	—
1186	C₂×C₄	—	8	2	no	—
1187	C₂×C₄	—	8	2	no	—
1188	C₂×C₄	—	8	1	no	—
1189	C₂×C₄	—	8	2	no	—
1190	C₂×C₄	—	8	1	no	—
1191	C₂×C₄	—	8	1	no	—
1192	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1193	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1194	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1195	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1196	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1197	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1198	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1199	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1200	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1201	C₈	—	2	1	no	—
1202	C₈	—	2	1	no	—
1203	C₈	—	2	1	no	—
1204	C₈	—	2	1	no	—
1205	C₈	—	2	2	no	—
1206	C₈	—	2	2	no	—
1207	C₇	#61198	1	1	yes	characteristic, direct product factor, Sylow
1208	C₂²	—	2	1	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	2	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	2	1	no	—
1214	C₂²	—	2	2	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	2	no	—
1219	C₂²	—	2	2	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	8	2	no	—
1229	C₂²	—	8	4	no	—
1230	C₂²	C₇×#546	1	2	yes	—
1231	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1232	C₄	—	2	2	no	—
1233	C₄	—	2	2	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	1	no	—
1236	C₄	—	2	2	no	—
1237	C₄	—	2	2	no	—
1238	C₄	—	4	2	no	—
1239	C₄	—	4	2	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	2	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	2	no	—
1245	C₄	—	4	1	no	—
1246	C₄	C₇×#546	1	2	yes	—
1247	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1248	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1249	C₂	—	2	2	no	—
1250	C₂	—	4	1	no	—
1251	C₂	—	4	1	no	—
1252	C₂	—	4	2	no	—
1253	C₂	—	4	2	no	—
1254	C₂	—	8	1	no	—
1255	C₂	—	8	1	no	—
1256	C₂	C₂×C₇×#546	1	1	yes	characteristic
1257	C₂	C₇×#3584	1	1	yes	characteristic
1258	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×#3493	C₂	semidirect
2. C₇×#3489	C₂	semidirect
3. C₇×#3328	C₂	semidirect
4. C₇×#3322	C₂	semidirect
5. C₇×#3321	C₂	semidirect
6. C₇×#3320	C₂	semidirect
7. C₇×#3315	C₂	semidirect
8. C₇×#3311	C₂	semidirect
9. C₇×#3303	C₂	semidirect
10. C₇×#3300	C₂	semidirect
11. C₇×#3137	C₂	semidirect
12. C₇×#3098	C₂	semidirect
13. C₂×C₇×#485	C₂	semidirect
14. C₇×#3084	C₂	semidirect
15. C₇×#3060	C₂	semidirect
16. C₇×#3056	C₂	semidirect
17. C₇×#3046	C₂	semidirect
18. C₇×#3013	C₂	semidirect
19. C₇×#3002	C₂	semidirect
20. C₇×#2951	C₂	semidirect
21. C₇×#2933	C₂	semidirect
22. C₇×#2898	C₂	semidirect
23. C₇×#2896	C₂	semidirect
26. C₂×C₇×#137	C₂²	semidirect
29. C₂×C₇×#131	C₂²	semidirect
34. C₇×#555	C₂²	semidirect
38. C₇×#552	C₂²	semidirect
45. C₇×#544	C₂²	semidirect
49. C₇×#537	C₂²	semidirect
59. C₇×#520	C₂²	semidirect
60. C₇×#520	C₂²	semidirect
62. C₇×#491	C₂²	semidirect
63. C₇×#489	C₂²	semidirect
64. C₇×#488	C₂²	semidirect
65. C₇×#487	C₂²	semidirect
68. C₇×#485	C₂²	semidirect
69. C₇×#485	C₂²	semidirect
70. C₇×#485	C₂²	semidirect
71. C₇×#484	C₂²	semidirect
72. C₇×#482	C₂²	semidirect
73. C₇×#480	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#476	C₂²	semidirect
77. C₇×#475	C₂²	semidirect
79. C₇×#470	C₂²	semidirect
80. C₇×#469	C₂²	semidirect
82. C₇×#467	C₂²	semidirect
83. C₇×#465	C₂²	semidirect
84. C₇×#465	C₂²	semidirect
85. C₇×#465	C₂²	semidirect
86. C₇×#464	C₂²	semidirect
87. C₇×#463	C₂²	semidirect
88. C₇×#462	C₂²	semidirect
89. C₇×#461	C₂²	semidirect
92. C₇×#452	C₂²	semidirect
94. C₇×#451	C₂²	semidirect
98. C₇×#449	C₂²	semidirect
100. C₇×#448	C₂²	semidirect
102. C₇×#440	C₂²	semidirect
103. C₇×#440	C₂²	semidirect
104. C₄×C₇×Q₁₆	C₂²	semidirect
105. C₄×C₇×D₈	C₂²	semidirect
108. C₇×#435	C₂²	semidirect
109. C₇×C₈×D₄	C₂²	semidirect
110. C₇×#428	C₂²	semidirect
111. C₂×C₇×#107	C₂²	semidirect
112. C₂×C₇×#106	C₂²	semidirect
113. C₇×#424	C₂²	semidirect
115. C₇×#419	C₂²	semidirect
116. C₇×#419	C₂²	semidirect
122. C₇×#417	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
128. C₇×#416	C₂²	semidirect
129. C₂×C₇×#103	C₂²	semidirect
130. C₂×C₇×#103	C₂²	semidirect
131. C₂×C₇×#103	C₂²	semidirect
132. C₇×#408	C₂²	semidirect
134. C₇×#405	C₂²	semidirect
135. #61198	C₇	direct (N × H)
322. #3493	C₂×C₇	semidirect
323. #3489	C₂×C₇	semidirect
324. #3328	C₂×C₇	semidirect
325. #3322	C₂×C₇	semidirect
326. #3321	C₂×C₇	semidirect
327. #3320	C₂×C₇	semidirect
328. #3315	C₂×C₇	semidirect
329. #3311	C₂×C₇	semidirect
330. #3303	C₂×C₇	semidirect
331. #3300	C₂×C₇	semidirect
332. #3137	C₂×C₇	semidirect
333. #3098	C₂×C₇	semidirect
334. C₂×#485	C₂×C₇	semidirect
335. #3084	C₂×C₇	semidirect
336. #3060	C₂×C₇	semidirect
337. #3056	C₂×C₇	semidirect
338. #3046	C₂×C₇	semidirect
339. #3013	C₂×C₇	semidirect
340. #3002	C₂×C₇	semidirect
341. #2951	C₂×C₇	semidirect
342. #2933	C₂×C₇	semidirect
343. #2898	C₂×C₇	semidirect
344. #2896	C₂×C₇	semidirect
509. C₂×#137	C₂²×C₇	semidirect
512. C₂×#131	C₂²×C₇	semidirect
517. #555	C₂²×C₇	semidirect
521. #552	C₂²×C₇	semidirect
528. #544	C₂²×C₇	semidirect
532. #537	C₂²×C₇	semidirect
542. #520	C₂²×C₇	semidirect
543. #520	C₂²×C₇	semidirect
545. #491	C₂²×C₇	semidirect
546. #489	C₂²×C₇	semidirect
547. #488	C₂²×C₇	semidirect
548. #487	C₂²×C₇	semidirect
551. #485	C₂²×C₇	semidirect
552. #485	C₂²×C₇	semidirect
553. #485	C₂²×C₇	semidirect
554. #484	C₂²×C₇	semidirect
555. #482	C₂²×C₇	semidirect
556. #480	C₂²×C₇	semidirect
557. #479	C₂²×C₇	semidirect
558. #478	C₂²×C₇	semidirect
559. #476	C₂²×C₇	semidirect
560. #475	C₂²×C₇	semidirect
562. #470	C₂²×C₇	semidirect
563. #469	C₂²×C₇	semidirect
565. #467	C₂²×C₇	semidirect
566. #465	C₂²×C₇	semidirect
567. #465	C₂²×C₇	semidirect
568. #465	C₂²×C₇	semidirect
569. #464	C₂²×C₇	semidirect
570. #463	C₂²×C₇	semidirect
571. #462	C₂²×C₇	semidirect
572. #461	C₂²×C₇	semidirect
575. #452	C₂²×C₇	semidirect
577. #451	C₂²×C₇	semidirect
581. #449	C₂²×C₇	semidirect
583. #448	C₂²×C₇	semidirect
585. #440	C₂²×C₇	semidirect
586. #440	C₂²×C₇	semidirect
587. C₄×Q₁₆	C₂²×C₇	semidirect
588. C₄×D₈	C₂²×C₇	semidirect
591. #435	C₂²×C₇	semidirect
592. C₈×D₄	C₂²×C₇	semidirect
593. #428	C₂²×C₇	semidirect
594. C₂×#107	C₂²×C₇	semidirect
595. C₂×#106	C₂²×C₇	semidirect
596. #424	C₂²×C₇	semidirect
598. #419	C₂²×C₇	semidirect
599. #419	C₂²×C₇	semidirect
605. #417	C₂²×C₇	semidirect
606. #417	C₂²×C₇	semidirect
611. #416	C₂²×C₇	semidirect
612. C₂×#103	C₂²×C₇	semidirect
613. C₂×#103	C₂²×C₇	semidirect
614. C₂×#103	C₂²×C₇	semidirect
615. #408	C₂²×C₇	semidirect
617. #405	C₂²×C₇	semidirect
1207. C₇	#61198	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3493	2
C₇×#3489	2
C₇×#3328	2
C₇×#3322	2
C₇×#3321	2
C₇×#3320	2
C₇×#3315	2
C₇×#3311	2
C₇×#3303	2
C₇×#3300	2
C₇×#3137	2
C₇×#3098	2
C₂×C₇×#485	2
C₇×#3084	2
C₇×#3060	2
C₇×#3056	2
C₇×#3046	2
C₇×#3013	2
C₇×#3002	2
C₇×#2951	2
C₇×#2933	2
C₇×#2898	2
C₇×#2896	2
#61198	7

Subgroups — C7×#61198 #13238414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61198 #13238414